the graph shows the distribution of the lengths (in seconds) of videos on a popular video - streaming site…

the graph shows the distribution of the lengths (in seconds) of videos on a popular video - streaming site. the distribution is approximately normal, with a mean of 264 seconds and a standard deviation of 75 seconds. sixteen percent of videos are shorter than what length? 39 seconds 114 seconds 189 seconds 339 seconds
Answer
Explanation:
Step1: Recall the empirical rule for normal distribution
The empirical rule states that for a normal distribution:
- Approximately (68%) of the data lies within (1) standard deviation of the mean ((\mu\pm\sigma))
- Approximately (95%) of the data lies within (2) standard deviations of the mean ((\mu\pm2\sigma))
- Approximately (99.7%) of the data lies within (3) standard deviations of the mean ((\mu\pm3\sigma))
The area to the left of (\mu - \sigma) is (\frac{100 - 68}{2}=16%)
Step2: Calculate the value of (\mu-\sigma)
Given (\mu = 264) seconds and (\sigma=75) seconds. We use the formula (x=\mu-\sigma) Substitute the values: (x = 264- 75) (x=189) seconds
Answer:
189 seconds